Some properties of N(k)-quasi einstein manifolds

초록

In this paper, an example of an N(k)-quasi Einstein manifold with closed associated 1-form is given. Also we show that if a quasi Einstein manifold (Mn1 1 , g1) and an Einstein manifold (Mn2 2 , g2) satisfy a certain condition, then the Riemannian product manifold (Mn, g) = (Mn1 1 × Mn2 2 , g1 + g2) is a quasi Einstein manifold. In particular, in N(k)-quasi Einstein case, we show that there exists a quasi Einstein product manifold (Mn, g) = (Mn1 1 × Mn2 2 , g1 + g2) but not an N(k)-quasi Einstein manifold, which consists of an N(k)-quasi Einstein manifold (Mn1 1 , g1) and an Einstein manifold (Mn2 2 , g2) satisfying the certain condition. Finally we study an N(k)-quasi Einstein manifold satisfying the condition R(U,X) G = 0. © 2013 Academic Publications, Ltd.

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